Preparation of 3-substituted 5-acetyl-N-(<Emphasis Type="Italic">β</Emphasis>-hydroxyethyl) pyrrolidones

Previously unknown 5-acetyl-3-alkyl-N-(β-hydroxyethyl)pyrrolidones have been synthesized by the reaction of γ-acetyl-α-alkylbutyrolactones with ethanolamine, and their semicarbazones and acetyl derivatives have been obtained.     

Profinitely generated Γ-modules

Theorems of homological definiteness of arbitrary -modules are proved which generalize similar results proved earlier for -modules of special type.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 86, pp. 157–161, 1979.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

EIT resonance features in strong magnetic fields in rubidium atomic columns with length varying by 4 orders

Electromagnetically induced transparency (EIT) resonances are investigated with the ⁸⁵Rb D₁ line (795 nm) in strong magnetic fields (up to 2 kG) with three different types of spectroscopic vapor cells: the nano-cell with a thickness along the direction of laser light L ≈ 795 nm, the micro-cell with L = 30 μm with the addition of a neon buffer gas, and the centimeter-long glass cell. These cells allowed us to observe systematic changes of the EIT spectra when the increasing magnetic field systematically decoupled the total atomic electron and nuclear angular moments (the Paschen-Back/Back-Goudsmit effects). The observations agree well with a theoretical model. The advantages and disadvantages of a particular type of cell are discussed along with the possible practical applications.     

8-Molybdogermanate of rhodamine 6G and its use for the photometric determination of germanium

A procedure was developed for determining germanium as a Rhodamine 6G-8-molybdogermanic heteropoly acid ion-pair complex in solutions obtained after germanium separation by solvent extraction from the matrix of various Ge-containing samples. The procedure accuracy was evaluated by determining germanium in a reference standard sample of steel after preliminary separation by solvent extraction. For the certified content equal to 1.1 × 10^-4% the found content was 1.1 sx 10^-4% (n = 10, RSD = 3.0%, andP = 0.95)     

Effect of microwave treatment on the kinetics of formation and morphology of calcium hydrosilicates

It was shown that microwave treatment improves kinetics of formation and morphology of calcium hydrosilicates obtained from the waste of boric acid production, borogypsum.     

Hyperfine Paschen-Back regime realized in Rb nanocell

A simple and efficient scheme based on a one-dimensional nanometric-thin cell filled with Rb and strong permanent ring magnets allows direct observation of the hyperfine Paschen-Back regime on the D(1) line in the 0.5-0.7 T magnetic field. Experimental results are perfectly consistent with the theory. In particular, with σ(+) laser excitation, the slopes of the B-field dependence of frequency shifts for all 10 individual transitions of (85,87)Rb are the same and equal to 18.6 MHz/mT. Possible applications for magnetometry with submicron spatial resolution and tunable atomic frequency references are discussed.     

Cooperative Lamb shift in an atomic vapor layer of nanometer thickness

We present an experimental measurement of the cooperative Lamb shift and the Lorentz shift using a nanothickness atomic vapor layer with tunable thickness and atomic density. The cooperative Lamb shift arises due to the exchange of virtual photons between identical atoms. The interference between the forward and backward propagating virtual fields is confirmed by the thickness dependence of the shift, which has a spatial frequency equal to twice that of the optical field. The demonstration of cooperative interactions in an easily scalable system opens the door to a new domain for nonlinear optics.     

Direct interband light absorption in a cylindrical quantum dot in quantizing magnetic field

In this paper the direct interband transitions in cylindrical quantum dot (QD) made of GaAs are studied in the presence of a magnetic field. Two models of QD confinement potential are discussed. For both models the expressions for absorption coefficients and dependencies of effective threshold frequencies of absorption on the value of applied magnetic field and on geometrical sizes of QD are obtained. The selection rules corresponding to different transitions between quantum levels are found.     

The problem of reconstructing a quasihomogeneous string from its part

We consider quasihomogeneous strings with piecewise constant density and derive the quasihomogeneity condition. For a small number of string components, we present explicit formulas for reconstructing a string from its part. For an arbitrary number of string components, we construct a theory of matrices of special form (that we call distinguished) and present an algorithm for string reconstruction from its part.